Volume rendering may allow three-dimensional (3D) volumetric data to be visualized. Volumetric data may consist of a 3D array of voxels, each voxel characterized by an intensity value which may typically pertain to color and opacity. Each voxel may be assigned a color (e.g., one of R (red), G (green), and B (blue)) and an opacity, and a 2D projection of the volumetric data may be computed. Using volume rendering techniques, a viewable 2D image may be derived from the 3D volumetric data.
Volume rendering may have been widely used in many applications to derive a viewable 2D image from 3D volumetric data of an object, e.g. a target region within a patient's anatomy. In some medical applications such as radiosurgery, an anatomical target region that moves, due to e.g. heartbeat or breathing of the patient, may need to be tracked. In these cases, a volume rendered animation of periodic motions such as respiration and heartbeat may be desirable.
A 3D volume dataset which varies over time may be considered to be a 4D deformable volume image. A number of methods may be used for volume rendering of 4D deformable volume images. These methods may involve one or more of the following approaches: representing a deformable volume using tetrahedrons that have freedom to move in 3D space; using a marching cube algorithm to convert volume rendering to surface rendering by finding small iso-surfaces in non-structural data; representing the volumetric dataset with a procedural mathematical function; and using a multiple volume switching method, in which all the intermediate volumes are generated before rendering.
Many of these approaches may tend to be very time-consuming, and some of them may require extra memory. Some of these approaches may be difficult to implement for medical images. Also, with some of these approaches, it may be hard to obtain smooth transitions between stages.